okay, gang. ideas day. i got a couple of objects. i got a styrofoam ball and i got a lead ball. which one is heavier?

the lead ball. the lead ball. well, you don't really have enough information to say. but let me ask you another question. which is more dense? the lead ball. what does it mean to say dense? more packed together. more packed together. more compact, right? more scrunched up. and isn't this lead ball, even without weighing it, you can tell this is more dense than this. so we're gonna talk about a definition, gang, and the definition is density. density, here we go. two kinds of density: mass density and weight density. we can say mass density is simply the amount of mass per volume, or weight density is simply weight per volume, okay? if i told you, for example, my lanai had a 200-pound rock, would that be a big deal?

not a big deal. a lot of people got 200-pound rock out in the rock garden, yeah. let's suppose a 200-pound rock, gang, is that big. ooh, that is a big deal. you don't be seeing rocks like that, okay? that is a very, very compactly, composed rock of high density. okay? a lot of weight and a little volume. so density is the ratio of those two, okay? it turns out like the density of water is one gram for every one cubic centimeter. cubic centimeter, about the size of the tip of your thumb, one gram per cc. sometimes people call cubic centimeter cc, especially medical types, cc, okay? or one kilogram per liter. thousand kilogram per liter. you know, liter's like a milk carton. okay? okay, one kilogram per liter or one gram per cc, that's the density of water. how about the density of a whole lot of water? one. i could ask you guys a question like this: which has the greater density, a teaspoonful of water or a lake full of water? and you guys would say...

same, same. you say same. some will say, "man, there's a lot more water in that lake." the density is... and you would say... density... yeah, but it takes up a lot more room. see, we talk about density, we're talking about one thing compared to the other. isn't that true? like you got a hershey bar. you're gonna--someone say, "hey, can i have some of your hershey bar?" and you give him a little, tiny piece, right, 'cause you're hungry. say, "hey, how come you got the most?" you say, "i give you the same density as i have. we both have the same density." isn't that true? the density of that little flake of chocolate, the same density as that big hunk that you're holding, yeah? so density different than weight, yeah? here's these two objects. i asked you before which of these is heavier. which of these two are heavier? hold them both. that would be the metal. the metal. the metal weighs more. can you try these? which of these weighs more? - this one. - the metal. why you say the metal? because it's all concentrating here and--

the thing. and this is all over-- it's like i feel the weight here. uh-huh. is this pushing down with more force in your hand, gang? yeah. seems like. feel that. more--pushing down with more force? more force? i'll tell you what, gang. it's not so much force that's important here. when we ask how much it weighs, we're talking about force. right? the gravity force. yeah? but we're gonna talk about another idea. and what's the other idea, gang? begin with a p. - pressure. - pressure. it turns out--watch this, gang. it turns out that this weighs considerably more. wanna see? no funny business. okay, gang, how about the book here? the book is exerting pressure against the table, right? it's also exerting force against the table. which is exerting more force, the book like this or the book like this? same.

more force. same. how many same? yeah. because a bathroom scale measures force, yeah? and if you put it on a bathroom scale, it'll be forcing down the same amount, yeah? how about pressure? more pressure, like this or like this? or like this? that, especially. yeah, the more concentrated the pressure-- do you know that a lady's high heel gives more pressure on the floor than an elephant's foot? they never tell you, "hey, you can't let those elephants come in here because they're gonna damage linoleum," but they do say, "ladies with high heels can't come in here "'cause the high heels will make a dent on linoleum, and an elephant won't dent it at all." so it turns out the concentration of force, that's pressure. but you know what we're gonna talk about here today? talk about liquid pressure. liquid pressure. and liquid pressure-- let's take this container for example. there's a pressure at the bottom of this flask of liquid, because there's a weight of water pushing down over the area of the bottom. so let's talk about the liquid pressure. i'll show that right here.

assume it's all the way full here, okay? here's my liquid. i got the pressure down at the bottom, which equals the weight per-- oops, i didn't define the pressure over here. force per area, right? pounds per square foot. newtons per square meter, okay? so, it's a unit of force over some area, huh? and over here, we have force per area. and the force that makes the pressure at the bottom of that tank, that force is the weight of the fluid over said area down there. but this weight of fluid can be re-expressed, because if density equals weight over volume, does it follow that weight equals density times volume? can you do that? so i can say where i have weight, i can just put density times volume over area.

but how about volume, gang? we wanna measure the volume of things. let's suppose i wanna measure the volume of this eraser. isn't it true that the volume of this eraser would be this distance multiply by that distance, multiply by that distance? wouldn't that be the volume? we're talking about volume in cubic centimeters, right? cube? huh, huh? so isn't this times this, the area? so, couldn't the volume be the area multiplied by this distance? couldn't the volume of this also be the area of the surface multiplied by the depth? or the area of the bottom multiplied by the depth? yeah? so i can write that up here. i'll put density times-- where volume is, i'm gonna put area, see, this area right here, yeah, multiplied by the depth.

i have area, area. are these areas the same? yeah, so they cancel out. seeing what i can say? liquid pressure equals the density of the liquid multiplied by its depth. ain't that neat? so, you know what that means? the deeper you go on liquid, the more the pressure is gonna be. makes sense? yeah. but here we're finding out its directly proportional, which means you go twice as deep in the liquid, the pressure gonna be twice as much. we're talking today only about the pressure of the liquid. it turns out the atmosphere up above is adding to that pressure considerably. it's adding enough pressure as if this were 10.3 meters more deep. the weight of the air pushes down too. but we're gonna forget about that and talk about that-- for now. we'll talk about that later and only talk today about the liquid pressure. so liquid pressure, density times depth.

what this means, if you go out and-- you're swimming, you swim 10 meters deep, certain pressure against your ears, right? how about you swim twice as deep? how much more water pressure? - twice. - twice. how about three times as deep? three times. sing to this. nine times as deep. nine times. nine times. get the idea? density times depth. or if you swim just as deep in saltwater, more pressure or less or the same? check your neighbor. how about it, gang? which you get more pressure, in the saltwater or freshwater? - saltwater. - why saltwater? - more dense. - because it's more dense. see, saltwater is a little bit more dense than freshwater. gang, i wanna show you the fact that liquid depends only on depth and density with this little device here. these are called pascal's vases. what i'm gonna do is i'm gonna fill up a tank over here,

a reservoir, and water is gonna flow from this reservoir into here. i'll raise this up, and i'll water come from here into here. okay, gang. this little marker reminds me how high that is and we have a reading that's about up to here. let me put a little red mark so we can where it is. it'll be something like that, yeah. okay. now, let's take this down. empty the vase and we'll put on a bigger vase and i'll show you something rather remarkable. okay? like this one. more volume, yeah? but i'm gonna fill it to the same depth, and guess what we're gonna be seeing, gang.

okay? it turns out this gauge is measuring the pressure over the height over here. but when the two heights become equal, then it'll indirectly tell us what the pressure is on the closer vase, the transparent one. so, a little higher. too much, too much, too much. and there we have same height and same pressure. isn't that nice? now, how can it be that this wider vase has the same pressure as the narrow one?

some will say, "well, because they're the same depth and that's what the rule is." but how about the pressure holding up the sides? where does that come from? the glass. it turns out water is coming down, hitting the side, doesn't the water push against the side of the glass? water pushes glass? newton's third law. glass pushes water. how hard? the same. just as hard as if it were--huh? let's try this. okay, one more time. see, the vase like that. this water is pushing down against the side, but the side is pushing back up against the water. how hard? just as if you had all the water right here.

so it turns out it really does only depend on the depth. let's see what happens with something like this. narrower, narrower tube. [laughter] and there we have it, gang. and we see what? [laughter] exactly the same pressure. isn't that neat? isn't that neat? you like, huh? mmm. huh, huh? doesn't physics always work?

[laughter] yeah. all right. you get the idea. hey, but, you know, this is kind of strange, that a little narrow tube like that can exert just as much pressure on the bottom as a wide one. how can we explain that, gang? let's look at the--this time we have a tube like this. okay? how can the pressure down at the bottom here be just the same as if it were all filled with water? it behaves the same, doesn't it? but there's no water here. it turns out that water pressure acts in all directions. so at this particular depth, the pressure is due to that surface-- i mean, that volume of water-- that weight of water above pushing down. but that's pushing in all directions, and some of those molecules of water scrunch against the glass. they scrunch pretty hard because there's a pressure pushing them, yeah? so they push up against the glass like that. if the water pushes against the glass, newton's third law tells you the glass pushes down against the water. how hard? the same. just as hard as if you had all water up there. so you know what? the bottom doesn't know the difference.

it's the depth to the free surface that counts. a beautiful demo i saw of this years ago was a guy had a barrel. there's a wooden barrel, these old wine barrels, and he filled it water. completely filled. and at the top, covering the top, had a hole there, put a pipe, the pipe went up, oh, several feet, put a funnel at the top of the pipe, took a bucket of water, smaller than this. climb the top, pour the water into the funnel, filled up-- [makes sounds] --guess what happened? [makes sound] barrel burst. the barrel burst because of the enormous pressure. and here's the bit. the pressure in this barrel is just the same as if he had filled it with that amount of water. it's just the depth to the free surface to where you are, that particular depth multiplied by the density of fluid, that's the liquid pressure. really, really neat. this idea that pressure depends on depth tells us why dams

are built the way they are. do you ever see a dam like this? good design or bad design? bad. very bad design because the pressure is greater against the bottom and that's where it should be thicker, not like that, yeah. so we find maybe dams like this, huh? so the pressure down here exerts a force that's great, great, great, great, and there's more force at the bottom than at the top so the dam is thicker down there, simply because why? you got more force of the water pushing against it. when i was a kid, i lived near lilly pond, massachusetts. and lilly pond had a dam like this. and in that dam, they had these little middle things sticking up like this that annoyed us kids. they were pieces of barrel like this. here is one, like one couple here and a couple here and a couple here. and what we wanted to do is we wanted to ride our bikes across the top of the dam, you know? and--and that kind of thing. but these darn things here prevented us from doing it.

and we knew it was a conspiracy between the old folks and us, right? and it turns out these little things here had a purpose. and we found out that purpose on a winter-- a spring, really, where we had a lot of snow that winter. there's a lot of water coming down from the hills and filled up that pond. the pond is getting deeper and deeper and the city workmen come out and they stuck some boards, like shelving boards, just pine lumber, one-inch pine lumber. it turns out right on those slots. and that's what they were. they were slots to hold some boards for when the dam got extra deep. and son of a gun, if that dam didn't fill up just up like that-- [makes sound] --and these boards are holding back tons and tons of water. we kids look at that and we say, "gee, if the board does that, what was the concrete for?" let me ask you a question. could it have made it with all that board? no. what would happen to the dam, honey? begin with s-p, end with loosh. [laughter] sploosh. okay? so it turn-- how about if a great, big ship comes by here? [makes sound] that board still gonna hold that water back?

if there's no-- answer ends with a p. yup. yup. now, if the water is moving-- [makes sound] --a lot of momentum of the water is gonna crash into the boat, that's different. but if the water is still, gets deeper and deeper, that water pressure against here depends only on the density of the water, which wouldn't change if boat came by, multiply by the depth of the water. so the pressure is not very deep down here at the board to keep getting less, less, less. so, not very much pressure. pressure depends on depth. where is your blood pressure greater, in your feet or in your ears? feet. how many people do you know with varicose ears? okay? it's the feet. you get more pressure in your feet. why do you have more pressure in your feet? 'cause your feet are deeper, your feet are deeper. how about if you walk on your hands? okay? you look at the veins in your hands, okay? stand on your hands and you see those veins standing way up. hold your hands above your head, you can't see the veins. it turns out the pressure, the blood pressure depends on how deep you are with respect to the pump.

the pump's right here, yeah? why is it when you get your blood pressure checked, they put the little doohickey on your arm, right here, right next to the arm, right, the ticker, huh? same depth. so the pressure in your arm here would be the same pressure here. but more pressure on your feet. next time you're doing that, stand on your arm-- get in the doctor's office and do a handstand. i said--tell them do it, they won't do it, okay? [laughter] that's not good. gonna talk about buoyant force. buoyant force. you walk into a pond and you grab a big boulder. and you can hold that boulder up pretty well as long as you're under the water, yeah? but you start to walk out of the pond, you carry the boulder with you, you find out the boulder gonna get heavy and heavier, yeah? some will say, "oh, the gravity is not pulling so hard in the water." what do you think? yeah. it turns out, under the water, the boulder seems to be lighter. i can show you that here. here's a boulder or a piece of metal, yeah?

and it's got a certain weight. but what happens when i put this in water? the weight goes down. is that because gravity is being shielded? answer ends with a o. no. it begins with a n. - no. - try it. - no. - no. okay. it turns out it's being buoyed up. it's being buoyed upward. and what's making it buoy upward? so there's a force lifting it. why does the force of the displaced water lift it? nobody knows. believe or not believe? - we gonna be known, right? - that's right. et's take a look at this a little more carefully. you put this object under water,

any water pressure against the top? - yes. - yep. and that water pressure against the top gives a force against the top. any water pressure against the bottom? yeah. and that water pressure is gonna give a force against the bottom. liquid pressure acts on all directions. all directions. but the force is acting all directions that they conspire to act in one particular direction like this, the result is like that. hey, why do i draw that arrow longer here than here? it's deeper. the longer arrow means the force of water against the bottom is more, yeah? why would it be more down here? one reason. - depth. - it's deeper. this part of the water is deeper than here, so there's more force here. next time you're swimming-- you're swimming in the water, you're being held up by the water, right? dig on this idea. that water pressure is pushing harder on your bottom, the deeper part of your body than up here. and that's what holds you up. and that's the buoyancy. this difference in forces is what we call buoyant force. and the buoyant force acts upward. can you see why?

because this part here is stronger than this part, so there's a net forced up. how about sideways? i should be careful to draw these arrows so they're longer than this one and shorter than this one, yeah? but why is it an object is not buoyed sideways? they cancel out. they don't cancel out like this, but they cancel out like that. and that difference in forces gives rise to a buoyant force. and that's why this was lighter. so there's particularly more force of water pushing up against the bottom than the top, and it kinda lifted it. and you saw the scale reading was less. kinda neat, huh? and there's a reason for that, too. let's talk about liquid displaced. you better get this idea down first. here's an overflowed can. i'm gonna pour water in here until it's-- [laughter] --until it's just about right.

well... [laughter] nothing like a very smooth lecture, gang. [laughter] now, here's the bit. if i want to measure the volume of this, i could measure the area and multiply by the depth, and i could have the volume. but there's an easier way, especially for something irregular like a rock or something. and all you do is you dunk it in a can that's just at the verge of overflowing, like this, and water is being displaced. see? this is taking up the room of some of the water. i'm displacing water. now, i got a question for you, gang. what's the volume of water displaced compared to the volume of this? - the same. - same. something big will displace a lot of water. something little will displace a little water.

in fact, you could measure the volume right off from the side here. it looks like it's a little bit more than 300 milliliters, and you've got the volume. ain't that nice? like a measuring cup, yeah? so any type object-- volume can be measured in this simple way. kinda makes sense, doesn't it? now, what i'm gonna do is this. i'm gonna repeat-- what i'm gonna do-- what i hope to do-- [laughter] --is i'm gonna dunk this in the water. and when i do that, this weight reading will go down, yeah? i mean, i can kinda show you over here. the weight reading does go down. would you say this-- that that loss of weight was equal to the support force? and that support force, we have a name for, it begins with b, f.

- buoyant force. - buoyant force, okay? so the buoyant force can be seen by the loss of weight. i can't read that now, but read it now. read it now. subtracted to, there's a buoyant force, yeah? all right? i'm gonna do it over here on this overflow can, but i'm gonna catch the water that's displaced and i'm gonna weigh it. oops. [laughter] this is not gonna be perfectly accurate, okay? but note now what the reading is of just holding it. it looks like a little bit more than one newton holding up the empty cup. now, i dunk this in. this is losing weight, yeah? it's because i'm bringing-- i'm displacing more and more water. there now. this has lost all the weight it can lose. this is still catching water. i want you to compare how much weight did this lose, the suspended weight, and how much weight did this gain. the same. do you see that they're the--

same. --same. and that brings us to a very important rule with fluids. and that's this, that the buoyant force that acts on a submerged object is numerically equal to the weight of fluid displaced by the object, okay? i didn't say the buoyant force is equal to the weight of the object over here. it's the buoyant force equal to the weight of fluid, in this case, water displaced by the object. okay? we see that? that's called archimedes principle. archimedes principle, a very, very important principle. archimedes principle is named after a person, no longer with us, a greek from long, long ago, and his name was aloysius j. principle. principle, all right. yes, good. [laughter] in honor of--who's buried in grant's tomb? ulysses s. tomb. - tomb. - tomb. that's right. that's why we call it grant's tomb, right? okay. who's main street named after? mister who?

street. mr. street. you got it. all right. all right. physics types. we're hot today. if you'd be understanding this, you can answer this kind of question. well, let's s put it right back over in here. i'm gonna take a baseball, and i'm gonna put the baseball right here. and i'm gonna let the baseball sink a little deeper to here, and then finally to here. this is position "a," position b, position c. i got a question for you. at which position, "a," b or c, does the baseball experience the greatest pressure? c. check your neighbor. c. because it's deeper. greatest pressure.

how many say it's c because it's deeper? how many say, "no, it's a trick question, hewitt. it turns out to be the same at all positions." show of hands. good, good. wonderful, wonderful. let's try this question. at which position, "a," b or c, does the baseball experience the greatest buoyant force? - "a." - check the neighbor. force down is smaller. also the force up-- what's the answer, gang? "a." how many say same everywhere? show of hands. well, let's see who's who. let's pass a piece of paper around. how many people say, "no, it turned out "the buoyant force can be greater at c because it's deeper?" show of hands. it's down. how many say... [laughter] how many say it's the same everywhere? how many are not quite so sure? how many say, "hewitt, i'm sure of everything. by gosh, count me in." okay? [laughter] well, it turns out, gang, it's gonna displace the same amount of water at which position? all.

same everywhere. see? when i dunk this object in here, you see it lose some weight when it gets to here, right? does it lose more weight here? does it lose more weight here? isn't the weight that's lost the same at all points? isn't there more pressure when it's down here? if the pressure is greater than up here, true or false? true. so there's more pressure pushing up against the bottom down here? yup. there ought to be then more buoyancy? except down here, there's also more pressure pushing against the top-- right. --than when you're over here. - right. - and so guess what, gang? it's the pressure difference. the difference between the pressure pushing the bottom here and here, that difference is the same as the smaller pressure pushing here

versus the even smaller pressure pushing here. so the difference in pressure is the same at any depth. but you can short-circuit the whole thing by just saying, hey, gang, the buoyant force is numerically equal to the weight of water displaced. it's displacing the same amount of water at every point. look, that level stays the same. it's not till i take it out that it falls, okay? so i'm displacing the same amount of water. ain't that nice? ain't that nice? okay. yeah. so as you're swimming and you're swimming deeper and deeper, does the buoyancy stay the same on you? i wonder how many people have drowned with that idea. [laughter] you know, ordinarily, when swimming-- you're swimming under the water, right? you're kinda swimming under the water. you're in a pool, just a few feet deep, right? you're swimming, yeah. you kinda stop and you kinda come down like this, like you keep going out there, okay, and you stopped, and you kinda bob to the surface. isn't that true? that's because the buoyancy acting on you turns out to be a little bit greater than your weight. so the net force is up. but i often wondered what happens to someone

who swims very, very deep, maybe closing their eyes 'cause the water's smarting their eye. and they're very, very deep. and they stop and they keep-- they just wait until they bob to the surface and they wait, they wait, they wait, they wait and clunk. oh, gosh. [laughter] then you're all out of breath. because it turns out when you get deeper and deeper, you don't get as much buoyancy acting on you. can anyone figure out why? really, really deep, the pressure gonna be more? more. do i change the volume of this with more pressure? no. not very much. how about like a balloon? very much. how about--aren't you a little bit like a balloon? you got lungs, honey? air in the lungs. can that air be compressed? - yeah. - huh? so what happens to your volume as you go deeper and deeper? smaller. you get scrunched up, so the buoyancy gets more or less? - less. - less. and it might not be enough to bring you back to the surface. so if that baseball got squashed up, then the buoyancy would be less deeper.

but if it stays the same size, then it doesn't. kinda neat, huh? got a little thought experiment, gang. a little thought experiment. see this great, big cubic block of lead right here? very, very heavy. see it? see this other cubic block over here of aluminum? they look the same, don't they? notice--both are painted. what color are they painted? green. again. green. green. yeah, they're painted green. can you see they're both the same shade of green? how many people can't see they're the same shade of green? how many-- "i can't use my imagination?" [laughter] who? they're both green. in fact, they're the exact same-- they look exactly the same, don't they? but if you try to move them, you can find out which one is lead, yeah? now, i take these both identical volume blocks and i, boom, i push them into the water. [makes sounds] they sink.

you got to tell me, which one got the greatest buoyant force? the lead, the humongously heavy lead, or the light aluminum? - same. - check the neighbor. how many say the buoyant force is greater on the lead? how many say it's the same on each? how many say, well-- how about it, gang? it turns out it's the same on each. you know why? same color. because they both have the same color. [laughter] all right. hey. same color, all right. anything with that shade of green will have the same buoyancy. no, it's the same volume, yeah? 'cause the same volume displaces the same amount, okay? can we continue further? again, i've got the lead block. this block over here looks like it's aluminum painted green, right? but it's not. you know what it is?

it's a styrofoam block. but you know what? it looks to you--doesn't it look to you to be the same? it has the same size, styrofoam, lead. i push them in the water. [makes sounds] one sinks. the other one doesn't. i got a question for you. upon which is the buoyant force greater? on the styrofoam or on the lead? check your neighbor. okay, gang. how many say same, same? how many say there's more buoyant force on the lead?

no, there's more buoyant force in the styrofoam. that's why it floats. none of the above. [laughter] how about it, gang? how about it? which one? lead. is it the lead? the styrofoam displaces the amount of its weight, same amount of water-- i got a question for you, gang. i got a question for you. you got a ship and the ship is loaded with iron. what's gonna happen to the way that ship floats? sink deeper. it's gonna sink deeper, yeah? how about if you got a ship loaded with styrofoam? - what happens? - it's gonna sink deeper too. what's this with floating anyway? yeah. how come this piece of clay sinks? some would say, "because there's no buoyant force acting on it." true or false?

- false. - false. there is a buoyant force acting on the clay that's submerged in this colored water, okay? but the buoyant force is how big compared to the weight? less. how many say, "when you drop it, ah, the weight is obviously greater than the buoyant force?" how many are starting to be able to think like that? or how many people say, "well, i will remember what is going on and try to regurgitate it as best i can?" no, no, no. you can see that, honey, the fact that it went down, the weight must have overpowered the buoyant force. how can i make the buoyant force bigger? by displacing more water. i suppose i take the clay. and now, i shape it such that when i put it in the water, it will displace more water. let's see if it displaces more water. no, it doesn't. okay? not yet. the buoyant force is not big enough. i'd have to make the volume bigger. oh, i really can't make the volume bigger like styrofoam is all puffed up. but what i can do is i could shape it into the shape of a bowl and make out of it of guess what?

begin with a b. - boats. - end with oat. okay? a boat. if you told people few centuries ago that you were gonna make a boat made out of iron, honey, they would look at you like you were bonkers, because iron doesn't float. people made boats out of wood. well, here's this clay. it has the same weight. watch this. oh, yeah. [laughter] yeah, look at it now, gang. [laughter] isn't that nice? now, it's being held up by what? - your fingers. - your hands. my fingers. you get the idea. more about his next time. but what i wanna ask you next time for homework is this. i wanna ask you, if you have a ship that's loaded with styrofoam, will that ship float higher, lower or the same as if the ship were empty?

so a ship loaded with a cargo of styrofoam will float higher in the water, the same level in the water, or lower in the water than the same ship with no cargo? that's your question for homework for next time. okidok? see you then. [music] captioning performed by aegis rapidtext